1. Field of the Invention
The present invention relates to computerized simulation of hydrocarbon reservoirs, and in particular to simulation of wellbore flow in reservoirs with complex multi-lateral wells tightly coupled with thousands of reservoir grid cells in a large high resolution reservoir simulation model.
2. Description of the Related Art
Reservoir simulation is widely used in the petroleum industry to analyze by computerized processing the performance of subsurface hydrocarbon reservoirs and to manage and optimize production from such reservoirs. One type of reservoir simulation is what is known as fully-coupled full-implicit well-reservoir simulation. Presently, most wells drilled are multilateral horizontal wells with long reach to increase reservoir contact. At the same time, finer grid reservoir simulation model are used to enhance the fidelity of recovery process analysis and better optimize and plan future reservoir management operations. As a result, it is not uncommon to have a multi-lateral well penetrating several thousand grid cells.
To properly model the physics of flow in and around the wellbore, the well may also be segmented to represent in detail the flow physics inside the wellbore. This in turns leads to more accurate boundary condition for the inflow performance calculation for fluids flow into and out of a well cell.
So far as is known, current art computerized fully-coupled fully-implicit reservoir simulators have used what are known as the Rowsum or Colsum approximations in the construction of the preconditioning step of the iterative solver of the simulator. This is because earlier methods than the Rowsum or Colsum approximations used either pre-elimination of the well equations using the reservoir equations, or direct application of a preconditioning method on the composite matrix with both the well and reservoir equations. However, these earlier methods were only suitable if the numbers of grid cells penetrated by the wells were small.
Otherwise, the numbers of fill terms in the solution matrices of the earlier methods became too large and impractical. The earlier solver methods also in a number of cases were too complex to implement because the well equations and reservoir equations sets had different characteristics and difficulties. At the same time, the number of algebraic equations per well segment was typically different from the number of equations per reservoir grid cell. This complicated the solver book-keeping of processor node assignment and reservoir and well cell data distribution, and also reduced code complexity, impact on solution algorithm, as well as code efficiency.
The Rowsum or Colsum methods which came into use to replace earlier methods to account for the well influence matrix were simple to implement and were, as noted, typically used in current reservoir simulators. Unfortunately, this method was weak, and lacked the required robustness for the complex problems where a long-reach multilateral well might in normal cases penetrate thousands of grid cells. This was particularly true for a highly heterogeneous reservoir modeled with fine grids, and when the well might be cross-flowing, meaning that some of the well perforations may have fluid inflow into the wellbore while some other perforations may have backflow from the wellbore into the reservoir.